Asymptotic of mean values of multiplicative functions
type: Item
instance of: scholarly article
title: Asymptotic of mean values of multiplicative functions
zbMATH Open document ID: 0591.10037
DOI: 10.1007/BF01137460
author: S. T. Tulyaganov
published in: Mathematical Notes
publication date: 1985-01-01T00:00:00Z
review text: A number of authors, notably \textit{E. Wirsing} [Math. Ann. 143, 75-102 (1961; Zbl 0104.042)] and \textit{B. V. Levin} and \textit{A. S. Fajnlejb} [Usp. Mat. Nauk 22, No.3 (135), 119-197 (1967; Zbl 0204.065)], have obtained asymptotic formulae as well as quantitative estimates for the means \((l/x)\sum_{n\leq x}f(n)\) of multiplicative functions f, for which the behavior of \(f(p^ m)\) on average is known with sufficient accuracy. The present author proves a result of this type, which generalizes some of the earlier results. Its precise formulation is too complicated as to be stated here. It should be noted, however, that the author's result does not contain the deeper and better known mean value theorems of \textit{E. Wirsing} [Acta Math. Acad. Sci. Hung. 18, 411-467 (1967; Zbl 0165.059)] and \textit{G. Halász} [ibid. 19, 365-403 (1968; Zbl 0165.058)], in which, apart from some boundedness conditions, no a priori knowledge of the behavior of \(f(p^ m)\) is assumed.
Mathematics Subject Classification ID: 11N37
Mathematics Subject Classification ID: 11K65
zbMATH DE Number: 3948396
zbMATH Keywords: asymptotic formulae
zbMATH Keywords: multiplicative functions
zbMATH Keywords: mean value theorems
reviewed by: Adolf Hildebrand
MaRDI profile type: Publication
cites work: Q3048919
cites work: Application of sums of multiplicative functions to the study of large deviations
cites work: Das asymptotische Verhalten von Summen über multiplikative Funktionen. II
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description: scientific article; zbMATH DE number 3948396